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A131400 A046854 + A065941 - I (Identity matrix).

%I A131400 #8 Sep 08 2022 08:45:31
%S A131400 1,2,1,2,2,1,2,3,3,1,2,3,6,3,1,2,4,7,7,4,1,2,4,11,8,11,4,1,2,5,12,15,
%T A131400 15,12,5,1,2,5,17,16,30,16,17,5,1,2,6,18,27,36,36,27,18,6,1,2,6,24,28,
%U A131400 63,42,63,28,24,6,1,2,7,25,44,71,84,84,71,44,25,7,1
%N A131400 A046854 + A065941 - I (Identity matrix).
%C A131400 Row sums = A001595: (1, 3, 5, 9, 15, 25, 41, 67,...).
%H A131400 G. C. Greubel, <a href="/A131400/b131400.txt">Rows n = 0..100 of triangle, flattened</a>
%e A131400 First few rows of the triangle are:
%e A131400   1;
%e A131400   2, 1;
%e A131400   2, 2,  1;
%e A131400   2, 3,  3, 1;
%e A131400   2, 3,  6, 3,  1;
%e A131400   2, 4,  7, 7,  4, 1;
%e A131400   2, 4, 11, 8, 11, 4, 1; ...
%t A131400 With[{B = Binomial}, Table[If[k==n, 1, B[Floor[(n+k)/2], k] + B[n - Floor[(k+1)/2], Floor[k/2]]], {n,0,12}, {k,0,n}]]//Flatten (* _G. C. Greubel_, Jul 13 2019 *)
%o A131400 (PARI) b=binomial; T(n,k) = if(k==n, 1, b((n+k)\2, k) + b(n - (k+1)\2, k\2));
%o A131400 for(n=0,12, for(k=0,n, print1(T(n,k), ", ", ))) \\ _G. C. Greubel_, Jul 13 2019
%o A131400 (Magma) B:=Binomial; [k eq n select 1 else B(Floor((n+k)/2), k) + B(n - Floor((k+1)/2), Floor(k/2)): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jul 13 2019
%o A131400 (Sage)
%o A131400 def T(n, k):
%o A131400     b=binomial;
%o A131400     if (k==n): return 1
%o A131400     else: return b(floor((n+k)/2), k) + b(n - floor((k+1)/2), floor(k/2))
%o A131400 [[T(n, k) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Jul 13 2019
%o A131400 (GAP)
%o A131400 B:=Binomial;;
%o A131400 T:= function(n,k)
%o A131400     if k=n then return 1;
%o A131400     else return B(Int((n+k)/2), k) + B(n - Int((k+1)/2), Int(k/2));
%o A131400     fi;
%o A131400   end;
%o A131400 Flat(List([0..12], n-> List([0..n], k-> T(n,k) ))); # _G. C. Greubel_, Jul 13 2019
%Y A131400 Cf. A046854, A065941, A001595.
%K A131400 nonn,tabl
%O A131400 0,2
%A A131400 _Gary W. Adamson_, Jul 06 2007
%E A131400 More terms added by _G. C. Greubel_, Jul 13 2019